What is the Si unit of energy?

Answer

To determine the SI unit of energy, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Energy and Work**:
- Energy is defined as the capacity to do work. Therefore, the SI unit of energy will be the same as the SI unit of work.

2. **Defining Work**:
- Work is defined mathematically as the product of force and displacement:
\[ \text{Work} = \text{Force} \times \text{Displacement} \]

3. **Identifying the Units of Force and Displacement**:
- The unit of force can be derived from Newton's second law, which states that force is mass times acceleration:
\[ \text{Force} = \text{Mass} \times \text{Acceleration} \]
- The SI unit of mass is kilograms (kg).
- The SI unit of acceleration is meters per second squared (m/s²).

4. **Calculating the Unit of Force**:
- Therefore, the unit of force (Newton) can be expressed as:
\[ \text{Unit of Force} = \text{kg} \times \text{m/s}^2 = \text{kg} \cdot \text{m} \cdot \text{s}^{-2} \]

5. **Identifying the Unit of Displacement**:
- The unit of displacement is simply meters (m).

6. **Combining Units to Find Work**:
- Now, substituting the units of force and displacement into the work equation:
\[ \text{Unit of Work} = \text{Force} \times \text{Displacement} = (\text{kg} \cdot \text{m} \cdot \text{s}^{-2}) \times \text{m} \]
- This simplifies to:
\[ \text{Unit of Work} = \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2} \]

7. **Conclusion**:
- Since the unit of work and energy are the same, the SI unit of energy is:
\[ \text{Joule (J)} = \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2} \]

### Final Answer:
The SI unit of energy is the Joule (J), which is equivalent to kg·m²/s².

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